Question: Rewrite as a simplified fraction. ${3.89\overline{7} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3897.7777...\\ 100x &= 389.7777...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3508}$ ${x = \dfrac{3508}{900}} $ ${x = \dfrac{877}{225}} \text{or} {3 \dfrac{202}{225}}$